This invention concerns an arrangement for providing favorable fuel consumption during acceleration of a vehicle engine. An arrangement which achieves favorable fuel consumption is disclosed in U.S. Pat. No. 3,916,854. In this teaching, the engine accelerates in conformity with a predetermined favorable consumption curve in the power-speed diagram, independently of the instantaneous position of the accelerator pedal (hereinafter designated as accelerator pedal position), until the adjustment of the control means of the fuel metering device given by the accelerator pedal position is achieved. The control means might be the throttle valve in a carburetor or the control rod in a fuel injection pump. Then the actual consumption is predetermined by the curve of constant position of the control means (i.e. constant accelerator pedal position) in said diagram.